In case of importance node pruning, the nodes with lowest absolute value of outgoing edges are dropped. Following [1]} the outgoing weights of all the hidden teacher nodes are equal (we call it \(v^*\) ). Also, from Lemma REF  we see that the sum of the weights of the outgoing edges of the student nodes which learn the same teacher node add up to the outgoing edge weight of the corresponding teacher hidden node. Moreover, we assume the ansatz \(v_i = v_j\)  when \(i,j \in G_n\) , where \(G_n\)  denotes the set of student nodes which learn the same teacher node \(t_n\) . Hence, we can see that all the outgoing edges are approximately similar. We also verify this fact experimentally. Therefore, this defines an approximately uniform distribution on the set of hidden nodes. Hence, this is almost same as random node pruning and so the result follows from Theorem .
